Answer :

Answer:

x = - 9 , x = 1

Step-by-step explanation:

given

[tex]\frac{x-3}{x}[/tex] = [tex]\frac{-8}{x+3}[/tex] ( cross- multiply )

(x - 3)(x + 3) = - 8x ← expand left side using FOIL

x² - 9 = - 8x ( add 8x to both sides )

x² + 8x - 9 = 0 ← quadratic equation in standard form

(x + 9)(x - 1) = 0 ← in factored form

equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x - 1 = 0 ⇒ x = 1

the solutions to the equation are x = - 9 and x = 1

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Rewritten by : Barada